Geodesic
Positive scalar curvature on foliations
Weiping Zhang1
1 Chern Institute of Mathematics & LPMC, Nankai University, Tianjin, P. R. China and Center for Applied Mathematics, Tianjin University, Tianjin, P. R. China
Annals of mathematics, Tome 185 (2017) no. 3, pp. 1035-1068.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We generalize classical theorems due to Lichnerowicz and Hitchin on the existence of Riemannian metrics of positive scalar curvature on spin manifolds to the case of foliated spin manifolds. As a consequence, we show that there is no foliation of positive leafwise scalar curvature on any torus, which generalizes the famous theorem of Schoen-Yau and Gromov-Lawson on the nonexistence of metrics of positive scalar curvature on torus to the case of foliations. Moreover, our method, which is partly inspired by the analytic localization techniques of Bismut-Lebeau, also applies to give a new proof of the celebrated Connes vanishing theorem without using noncommutative geometry.
DOI : 10.4007/annals.2017.185.3.9

Weiping Zhang 1

1 Chern Institute of Mathematics & LPMC, Nankai University, Tianjin, P. R. China and Center for Applied Mathematics, Tianjin University, Tianjin, P. R. China 
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Weiping Zhang. Positive scalar curvature on foliations. Annals of mathematics, Tome 185 (2017) no. 3, pp. 1035-1068. doi : 10.4007/annals.2017.185.3.9. http://geodesic.mathdoc.fr/articles/10.4007/annals.2017.185.3.9/

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